Primitivity and independent sets in direct products of vertex-transitive graphs
نویسندگان
چکیده
منابع مشابه
Independent sets in direct products of vertex-transitive graphs
Let G and H be two vertex-transitive graphs. It is easy to find that α(G × H) = |G||H | 2 if one of them is a bipartite graph. In this paper, we will identify the structure of the maximal-sized independent sets in G×H when one of them is a bipartite graph.
متن کاملIndependent sets of maximal size in tensor powers of vertex-transitive graphs
Let G be a connected, non-bipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G×G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif [8].
متن کاملIndependence and coloring properties of direct products of some vertex-transitive graphs
Let α(G) and χ(G) denote the independence number and chromatic number of a graph G respectively. Let G×H be the direct product graph of graphs G and H . We show that if G and H are circular graphs, Kneser graphs, or powers of cycles, then α(G ×H) = max{α(G)|V (H)|, α(H)|V (G)|} and χ(G×H) = min{χ(G), χ(H)}. AMS Classification: 05C15, 05C69.
متن کاملVertex-transitive CIS graphs
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2010
ISSN: 0364-9024
DOI: 10.1002/jgt.20526